Simplify the following expression and state the condition under which the simplification is valid. $q = \dfrac{a^2 - 16}{a + 4}$
Answer: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = a$ $ b = \sqrt{16} = 4$ So we can rewrite the expression as: $q = \dfrac{({a} + {4})({a} {-4})} {a + 4} $ We can divide the numerator and denominator by $(a + 4)$ on condition that $a \neq -4$ Therefore $q = a - 4; a \neq -4$